Standard generators of L2(227) are a of
order 2, b of order 3 such that ab has order 227.
Standard generators of the double cover
2.L2(227) = SL2(227) are preimages
A and B such that B has order 3 and
AB has order 227.

Standard generators of L2(227):2 = PGL2(227) are not yet defined.
Standard generators of the double cover 2.L2(227):2 = 2.PGL2(227) are not yet defined.